y^2=(xy-x^2)dy/dx
y^2/x^2=(y/x-1)dy/dx
y/x=u
dy=udx+xdu
u^2=(u-1)(u-xdu/dx)
u^2/(u-1)=u-xdu/dx
xdu/dx=u-u^2/(u-1)
xdu/dx=-u/(u-1)
du/[u/(u-1)]=-dx/x
u-lnu=-lnx+C
y/x-ln(y/x)=-lnx+C
令u=y/x,dy=udx+xdu,代入化简得到
（1-1/u）du=dx/x
积分得
lnxu=u+c'
xu=Ce^u
y=Ce^(y/x)
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024